ENERGY 1! 5. How many cubic miles of ice could be melted by the heat comput in the preceding problem? The latent heat of ice is 80 calories per gra: 6. The winder of a spinning top is a helical spring, which is set in cylindrical piece 1 inch in diameter. When the winder is hooked to t top and twisted through TT radians a force of 1 pound has to be applied the cylinder tangentially in order to keep it from untwisting itself. Af1 the spring is given a twist of^J turns the top is released. Find the kine-energy the top would acquire if there were no frictional forces. 7. In the preceding problem find the angular velocity of the top suppc ing it to consist of a circular plate of 2 inch radius, and of J pound weig] 8. If the top of the preceding problem turns for 2 minutes before stc ping, find the mean torque due to friction and resistance; also find t total number of revolutions made. 9. A top is given a motion of rotation by pulling at a string wou: around it. Derive an expression for the energy communicated, (a) wh • the force applied to the string is constant; (b) when it varies directly wi the length of the string which is unwound. POWER. 157. Power. — Power is the rate at which work is don When put into the language of calculus this definition b comes P = ^- (VI at Power is a scalar quantity and has the dimensions [ML2T~ The C.G.S. unit of power is the erg per second. This ui is too small for engineering purposes; therefore two larg units are adopted, which are called the watt and the kilowa The following relations define these units : -, <L<L 1 joule 1 watt = —~ -1 sec. sec. 1 kilowatt = 103 watts = 1010- sec.